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3.2.2—Vmax and Km

Syllabus
9700–2028–2029
Objective
3.2.2
Level
AS

Read Vmax and Km from a substrate-saturation curve

On a graph of initial reaction rate, v, against substrate concentration, [S], Vmax is the capacity ceiling approached when the enzyme’s active sites are saturated. Km is the substrate concentration at which the initial rate is half of Vmax.

v=Vmax⁡2when[S]=Kmv=\frac{V_{\max}}{2}\quad\text{when}\quad [S]=K_m

  1. Find Vmax: Inspect the high-[S] plateau or limiting value approached by the curve; this is the estimated Vmax.
  2. Find half Vmax: Mark the y-value halfway between zero and Vmax.
  3. Read Km: Move horizontally from half Vmax to the curve, then vertically to the [S] axis. That x-value is Km.
  4. Explain the shape: At low [S], adding substrate raises productive complex formation. At high [S], most active sites are occupied, so the curve flattens toward Vmax.

Worked read-off: if a curve approaches a clear plateau, label that plateau Vmax, mark its midpoint on the rate axis, and project from the midpoint through the curve to the substrate axis. The substrate-axis reading at that intercept is Km; do not read Km at the plateau itself.

Km is not the substrate concentration at Vmax. A lower Km can indicate higher apparent affinity only when the same model and comparable conditions apply; Vmax also depends on the amount of active enzyme. Read initial-rate data and do not invent precision beyond the graph.

Follow the limiting step across the topic

A rate change is evidence about the current bottleneck, not an explanation by itself. Ask whether the observation is best explained by collision frequency, substrate availability, usable active-site capacity, enzyme shape or diffusion.

  • A substrate plateau shows that enzyme capacity now limits rate; the plateau approaches Vmax.
  • Half of Vmax locates Km on the substrate-concentration axis.
  • If more substrate restores the original maximum, competition for active sites is supported.
  • If the maximum remains lower, functional enzyme capacity has been reduced.
  • If immobilised enzyme appears slower, diffusion may be limiting even though reuse and separation improve.

To make a valid conclusion, change one factor, control the others, compare initial rates and stay within the tested range. A single point cannot establish a curve shape or inhibitor type.

ConceptA-Level CAIE Biology AS